Summary
A fundamental requirement for the design of feedback control systems is the knowledge of structural properties of the plant under consideration. These properties are closely related to the generic properties such as controllability. A sufficient condition for controllability of polynomial switched systems is established here. Control design for nonlinear switched control systems is known to be a nontrivial problem. In this endeavor, an indirect approach is taken to resolve the control design problem pertaining to polynomial switched systems satisfying the aforementioned sufficient condition for controllability; it is shown that trajectories of a related controllable polynomial system can be approximated arbitrarily closely by those of the polynomial switched control system of our interest.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ezzine, J., Haddad, A.H.: Controllability and observability of hybrid systems. Int. J. of Control 49(6), 2045–2055 (1989)
Hermann, R.: On the accessibility problem in control theory. In: Int. Symp. on Nonlinear Differential Equations and Nonlinear Mechanics, pp. 325–332. Academic, New York (1963)
Jurdjevic, V., Kupka, I.: Polynomial control systems. Mathematische Annalen 272(3), 361–368 (1985)
Li, Z.G., Wen, C.Y., Soh, Y.C.: Switched controllers and their applications in bilinear systems. Automatica 37(3), 477–481 (2001)
Morse, A.S.: Supervisory control of famillies of linear set-point controllers, Part 1: Exact matching. IEEE Trans. on Automat. 41(10), 1413–1431 (1996)
Narendra, K.S., Balakrishnan, J.: Adaptive control using multiple models. IEEE Trans. on Automat. Contr. 42(2), 171–187 (1997)
Perera, P.C., Dayawansa, W.P.: Asymptotic feedback controllability of switched control systems. In: Proc. of the American Control Conference, pp. 239–244 (2004)
Stoer, J., Bulrisch, R.: Introduction to Numerical Analysis. Springer, New York (1980)
Szigeti, F.: A differential-algebraic condition for controllability and observability of time varying linear systems. In: Proc. of the IEEE Conf. on Decision and Control, pp. 3088–3090 (1992)
Williams, S.M., Hoft, R.G.: Adaptive frequency domain control of PPM switched power line conditioner. IEEE Trans. on Power Electronics 6(4), 665–670 (1991)
Zhendong, S., Ge, S.S., Lee, T.H.: Controllability and reachability criteria for switched linear systems. Automatica 38, 775–786 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Perera, P.C. (2009). Global Asymptotic Controllability of Polynomial Switched Systems and Their Switching Laws. In: Ghosh, B.K., Martin, C.F., Zhou, Y. (eds) Emergent Problems in Nonlinear Systems and Control. Lecture Notes in Control and Information Sciences, vol 393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03627-9_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-03627-9_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03626-2
Online ISBN: 978-3-642-03627-9
eBook Packages: EngineeringEngineering (R0)